If two fair coins are flipped, what is the probability that both show heads?

• A. 1/2
• B. 1/4
• C. 1/8
• D. 3/4

Answer: (B)

Two fair coins flipped involve independent events, so you multiply the chances for each coin. Each coin has two equally likely results, heads or tails, and together there are four equally likely outcomes: heads-heads, heads-tails, tails-heads, and tails-tails. Only one of these outcomes has both coins showing heads, so the probability is 1 out of 4, or 1/4. You can also get the same result by multiplying the individual chances: 1/2 for the first coin to be heads times 1/2 for the second coin to be heads equals 1/4. This matches the four-outcome view. The other numbers correspond to different events: 1/2 is the chance a single coin is heads, and 3/4 is the chance of at least one head in two flips. The correct probability is 1/4.